what does the rotation of a strong horizontal vortex into a vertical orientation form?

The rotation of a strong horizontal vortex into a vertical orientation forms a tornado (or tornado-strength vertical vortex) when other storm conditions are favorable.

What the phrase means

• A horizontal vortex is a tube of spinning air aligned roughly parallel to the ground, often created by strong wind shear in thunderstorms.

• When strong updrafts in a supercell thunderstorm tilt this horizontal spin into the vertical, that vorticity can concentrate and tighten into a vertical vortex, sometimes becoming a tornado.

From horizontal tube to tornado

• Wind shear first creates rolling, horizontal vortex tubes in the storm’s inflow region.

• The storm’s updraft tilts and stretches this horizontal rotation into a vertical column of spin, which can evolve into a tornado-scale vortex if the stretching and near-surface conditions are strong enough.

Important nuance

• Horizontal vortex tubes by themselves do not guarantee a tornado; they are one ingredient in tornadogenesis, alongside strong, persistent updrafts and supportive storm structure.

• In many storms, tilted horizontal vortices remain weak or disorganized and never form a tornado-strength vertical vortex.

TL;DR: Rotating a strong horizontal vortex into a vertical orientation, under the right supercell conditions, forms a vertically oriented vortex that can become a tornado.

Information gathered from public forums or data available on the internet and portrayed here.